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These Beautiful Images Are Created By Drawing Cardioids

These Beautiful Images Are Created By DrawCardioids
Hamid Naderi Yeganeh
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Mathematical artist

Mathematical artist
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Mathematical concepts are really powerful to make works of art. But we must try many mathematical functions in order to find formulas that produce very stunning images. Here I would like to share ten new mathematical artworks. I created these images by drawing thousands of cardioids. At the end of this post you can see the mathematical description of “4,000 Cardioids (2)”.

3,000 Cardioids (1)
3,000 Cardioids (1)
Hamid Naderi Yeganeh
2,000 Cardioids (1)
2,000 Cardioids (1)
Hamid Naderi Yeganeh
2,000 Cardioids (2)
2,000 Cardioids (2)
Hamid Naderi Yeganeh
3,000 Cardioids (2)
3,000 Cardioids (2)
Hamid Naderi Yeganeh
3,000 Cardioids (3)
3,000 Cardioids (3)
Hamid Naderi Yeganeh
2,000 Cardioids (3)
2,000 Cardioids (3)
Hamid Naderi Yeganeh
4,000 Cardioids (1)
4,000 Cardioids (1)
Hamid Naderi Yeganeh
2,000 Cardioids (4)
2,000 Cardioids (4)
Hamid Naderi Yeganeh
3,000 Cardioids (4)
3,000 Cardioids (4)
Hamid Naderi Yeganeh
4,000 Cardioids (2)
4,000 Cardioids (2)
Hamid Naderi Yeganeh

This image shows 4,000 cardioids. For each k=1,2,3,...,4000 the parametric equation of the k-th cardioid is:

z(t)=X(k)+iY(k)+S(k)(2e^(it)-e^(2it))e^(iT(k)),

where,

X(k)=cos(2πk/4000)((4/5)+(1/5)(cos(24πk/4000))^3),

Y(k)=sin(2πk/4000)((4/5)+(1/5)(cos(24πk/4000))^3),

S(k)=(1/20)+(1/8)(sin(24πk/4000))^2,

T(k)=18πk/4000.

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